Failure to meet payments on student loans guaranteed by the

Failure to meet payments on student loans guaranteed by the US government has been a major problem for both banks and the government. Approximately 50% of all student loans guaranteed by the government are in default. A random sample of 350 loans to college students in one region of the US indicates that 147 are in default. How much evidence do we have that the region differs from the national population?

No evidence

Some evidence

Strong evidence

Very strong evidence

Extremely strong evidence

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.42      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.026726124      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.993325909      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.002759549   [ANSWER]

It\'s up to you to decide on this one, maybe your class has set some standard on what is strong/very strong, etc.

But to me, this is very storng evidence. Please refer to the value fo P.